Page 253 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

1 3 R3
2. Let B =
-8 5 01
74 -3 1 0 2
TYPES OF MATRICES
Column matrix
(a) State the size of matrix B
3. (a)
(c)
-3 1
278
The matrix D =(0 0 00
2 7 8 -5 2 -5 2 p q
513
-5 2 -5 -25 2p q-05 82 p0 q8 r s
08 0808rs08 rs 1a -2
(b) State The matrix A = (5 ) is called a column matrix,
3 6 p
-5p2q-512apqpqr1sa xq (i) the elements in the first row
21
0r 8s 0x 8qr sr s x q
04
x q x q elements. A is a 2 x 1 matrix. -5 4 R1
p (iiq) the e1lemaents in1 thae second row
-5 4 R1 -5 4 R18 0 R2 has3runs
8 0 R2 ha8s30rowRs21 ha3s3Rro3ws
elements in two ways.
has 3 rows -8 -8 5 0
1 3 R3
1 3 R3
The matrix C =( 7 01
-5 4 R1
-4 )is called a square matrix, because it consists of the same number of rows as
8(i)07 R2
5 1
1 3 R3
columns, C is a 2 x 2 matrix. Null matrix
-(8ii) 45
01 01
(iii) -3 7 4 (iv)1
-8 5
74 74-31
0 (v)1 0
-31 -3102
(vi) 2
02 02 74
278 (b) 36 531633621 212104
) is called a null matrix, or zero matrix, because all the elements are zero.
State the order (or size) of the following
02278278513 matrices.
D is a 2 x 2 matrix
D is the identity matrix for the addition of 2 x 2 matrices.
Diagonal matrix
513513
0 36 251
4
0 4
8 5(d) 1
518 5 -2
78-2-45 0 70 -4 5 0 10 1 050 0 01 -20 0 1 0 0 1 0 -02 0 0 01 -2 0 1
0 1
014 585585
The matrix E =(5 0 0 -2
5
85 8 5 5 -2
5 85 7-4 00 50 10
q 1
a because it consists of a single vertical array of 1a1axq
rs xq5 xq85 5 85 7-4 00 50 10
8 0 R2 ha8s30runRs21 ha3s3Rru3ns
1 3 R3 11 3 R3 -2 0 1
(iii) the elements in the third row
Row matrix
0 0 0 -2 0 1 b + f
-5 4 R1
8 0 R2 has3runs
-5 4 R1
-5 4 R1 a -5b 4 Re1 8 e0 R2 ahasb2 columes e a + e
5) is called a row matrix, d + h
1(iv3)thRe3elementsinthefirstcolumn
8 0 R2 cha8sd20coluRmg21sha3s 2Rco3lucmsd
+=
1 3 R3 1 3 R3C1C2
g
-5 4 R1
elements. B is a 1 x 2 matrix. Square matrix
(v) the elements in the second column
C1 C2 C1 C2
8 0 R2 has 2 colums
1 3 R3 -5 4 R1
(c) -S5tate4theRp1osi-t5ion4ofeRac1h8of0theRf2ollohwasin3grows C1 C2
The matrix B = ( 8
h c + g
because it consists of a single horizontal array of
) is called a diagonal ab ee7-4ab00ee50a+1e0b+f
matrix, because it is a square matrix and all the a b e a e b c a e d b e g e a h e b c a e + d e e bg + a h + f e c b + + g f d + h
1 -2 c d g c h d
01 00 0-2 01 + += =
+=
c g d h g c h d c g + gh d + c h + g d + h
elements except the leading diagonal elements
are zero.
a b e e a b + e e = a +e b + f
c d g h c d g h c + g d+ h
247